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Policy Design in Long-run Welfare Dynamics
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Shows, in a stochastic model of welfare dynamics with decay and intervention returns, that Rawlsian (min-U, max-g) policies achieve higher long-run average welfare than utilitarian policies under survival and Matthew-effect conditions, with a reversal under a ruin condition.
Problem
Comparing Rawlsian and utilitarian social policies on long-run social welfare, given that policies that look suboptimal in the short run may yield larger long-term benefits.
Approach
Extends an attention-allocation model from industrial project management to welfare dynamics with individual-specific return and decay functions, proves closed-form long-run growth rates for Rawlsian and utilitarian policies, and gives a survival condition under which Rawlsian policies dominate (and a ruin condition under which utilitarian policies dominate), using a Lundberg-type inequality for s
Key results
- Under survival and Matthew-effect assumptions, Rawlsian min-U and max-g achieve long-run social welfare (M/N)f+ - ((N-M)/N)g-, exceeding utilitarian (M/N)f+ - ((N-M)/N)g+ almost surely.
- In SIPP-based simulations (206 individuals), Rawlsian policies have lower short-term welfare than utilitarian ones but overtake them after a few hundred timesteps.
- Under a ruin condition, the comparison reverses and utilitarian policies achieve better long-run welfare.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Rawlsian min-U/max-g instead of utilitarian max-U/max-f/max-fg under survival, Matthew-effect, and uniform-boundedness conditions | Welfare policy · Long-run welfare under survival condition | long-term social welfare | Helped |
| Use utilitarian policies instead of Rawlsian policies under the ruin condition | Welfare policy · Long-run welfare under ruin condition | long-term social welfare | Helped |
| Evaluate policies over a long horizon rather than a short horizon | Rawlsian versus utilitarian policies · SIPP simulations | social welfare | Mixed |
| Use random allocation instead of utilitarian allocation under survival conditions | Random policy · Long-run welfare under survival condition | long-term social welfare | Helped |
| Increase the budget M for random allocation | Random policy · SIPP simulations | convergence rate | Helped |
| Decrease b, strengthening the poor-get-poorer decay effect | Rawlsian min-U versus utilitarian max-U · Heterogeneous-population simulations | long-term social welfare | Helped |
| Change decay monotonicity from decreasing to constant | Rawlsian versus utilitarian policies · Survival condition, uniform bounds | long-term social welfare | No clear effect |
| Change decay monotonicity from decreasing to increasing | Rawlsian versus utilitarian policies · Survival condition, uniform bounds | long-term social welfare | Hurt |
| Change return and decay functions to constant | Rawlsian versus utilitarian policies · Survival condition, uniform bounds | long-term social welfare | No clear effect |
Surprising findings
- Rawlsian policies, despite being suboptimal in the short run, outperform utilitarian policies in the long run under the survival condition.
Limitations
- Results rely on uniform boundedness of return and decay bounds across individuals; heterogeneous cases are only studied by simulation.
- Simulations use simplified Gaussian-noise dynamics and welfare proxies from SIPP income bins.
Experimental setup
Datasets: Survey of Income and Program Participation (SIPP)
Metrics: long-term average social welfare (asymptotic growth rate) finite-horizon average welfare growth rate
Baselines: max-U (utilitarian) max-fg max-f max-g min-U (Rawlsian) random policy
Builds on: attention allocation model (staying with a winner / putting out fires) Lundberg's inequality
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